CALCIUM AND MAGNESIUM CARBONATES.
2001
T H E SOLUBILITY-PRODUCT CONSTANT OF CALCIUM AND MAGNESIUM CARBONATES. BY JOHN JOHNSTON. Received June 17, 1915.
I n connection with certain calculations undertaken primarily to ascertain what degree of purity of magnesium carbonate might be expected if i t were deposited by evaporation a t constant temperature of a solution containing both magnesium and calcium carbonates, i t became necessary to determine the appropriate solubility-product constants. Values of these quantities were calculated some years ago by Bodlander,* but these must now be revised because some of the constants employed by him are now known to be erroneous. Bodlander’s calculations for calcium carbonate were revised later by S t i e g l i t ~in , ~ connection with calculations relative t o the effect of a change in the amount of carbon dioxide in the atmosphere upon the proportion of calcium carbonate in gypsum deposited by the evaporation a t constant temperature of solutions (e. g., sea water) containing both. The available data have now all been recomputed so as to obtain really comparable values of these solubilityproduct constants which should be consonant with present-day knowledge of the various quantities involved in the calculations. With a knowledge of these constants one can make certain deductions which are important in relation to the question of the nature and character of the solid deposited when solutions containing both carbonates are evaporated down. The constant cannot be obtained directly from observations on the solubility of the carbonate M e 0 3 in pure water for two reasons: ( I ) because of the hydrolysis, the amount of which is in the first instance unknown; (2) because, as will be shown later, there cannot be true equilibrium except the solution be in contact, and have came to equilibrium, with a definite partial pressure of COz which must be measured. But if the partial pressure of COz is known, and the conqentration of the saturated solution in contact with i t (and with a definite solid phase) is deter4 mined, the solubility-product constant can readily be calculated. The equilibrium between the solid carbonate MC03,the solution, and an atmosFor a thorough discussion of this quantity see a series of 7 papers entitled “The Effect of Salts on the Solubility of Other Salts,” by A. A. Noyes, W. C. Bray, W. D. Harkins, and others, THIS JOURNAL, 33, 1643-86, 1807-73 (1911). Bodlander, 2. phxsik. Chem., 35, 23 (1900). a Stieglitz, “The Relations of Equilibrium between the Carbon Dioxide of the Atmosphere and the Calcium Sulphate, Calcium Carbonate, and Calcium Bicarbonate in Water Solutions in Contact with it.” In “The Tidal and Other Problems” by T. C. Chamberlin et d., Carnegie Inst. Publ. No. 107 (1909). This paper is not so widely known as it deserves to be, probably because no one would look in such a book for a paper dealing with such a topic.
2002
JOHN JOHNSTON.
phere in which the partial pressure of COZ is P , is determined completely by the following four equations, in all of which, and throughout this paper, symbols such as [MI represent the molar concentration of the species denoted by the symbol enclosed with.in the brackets : (I). [M++l[cos=l = K M (11). [H2CO,] = k'[COJ = c'P
(I) defines the solubility product K M ,which we wish to calculate; (11) expresses the equilibdum between the undissociated dissolved carbonic acid and the partial pressure P of the COz in contact with the solution; while (111)and (IV) define, respectively, the first and second ionization constants of carbonic acid in aqueous solution. At a given temperature the values of kl and kz, which are invariable, are known; the quantity c', which is a measure of the solubility of COz in the solution, varies, however, with the salt concentration of the solution. We shall now proceed to evaluate these constants. The Solubility of C 0 2 in Water and Salt Solutions. The absorption-coefficient CY of a gas, as given in tables of constants, is defined as the ratio of the volume of the. gas dissolved (reduced always to 0")to the volume of the water;' this ratio is, in accordance with Henry's law, independent of the pressure so long as the latter is not too high.
CiP
The molar concentration of the dissolved gas is then -,
when P is ex-
22.4
pressed in atmospheres; for 0 ( / 2 2 . 4 we shall write c. Now if we say that the concentratiorl of un-ionized carbonic acid [HzCO~]= cP, we make the tacit assumption that none of the COz exists as such in the solution, that all of it-apart )from the ions-is present as the hydrate HzC03. But, strictly speaking, the HzC03(which, of course, is also in equilibrium with its ionization products) is in equilibrium with the COz existing as such in solution and this in turn with the COz in the gas phase; i. e . , if n is the proportion of the total COz in solution existing as HzC03, [HzC03]/ [COZ]~ = %/(I - n ) , and [COz], = nz[COz]. On the other hand, as actually measured, c1 =
[H2Cos1-!r [cozls and therefore, from the above, c1 [ coz 1
=
[HzCO3] I [COZI n'
-___
Some authors give the solubility of the gas, which is the actaal volume of. gas a t the temperature in question absorbed by one volume of water; care must be taken to distinguish these two quantities.
CALCIUM AND MAGNESIUM CARBONATES.
2003
The value of n is not known, but Walker and Cormack' from a discussion of the matter, conclude that a t 18' it is almost certainly greater than 0 . 5 . We shall therefore write (V). [HE031 = nk [COZ]= ncP where G = a/22.4,and n, the proportion of the total CO2 in solution existing as H2C03,is greater than 0 . 5 ; we retain it, though it is unknown, in order to bring out the fact that the absolute value of certain of our constants depends upon the value assigned to n. The absorption of C 0 2 by water and aqueous solutions has been studied by several investigators with results which are satisfactorily concordant. Bohr2 determined it in water and in two solutions of NaC1-respectively I . 17 and 3 . 4 4 N-at temperatures ranging up to about 60'; Geffcken3 made measurements a t 15' and 25' of the solubility in 0 . 5 and I .o N solutions of a few salts and common acids. The change of absorptioncoefficient is nearly proportional to the salt concentration, and varies relatively little from one salt to another. I t is more nearly linear, and varies less for the several salts, when it is plotted against the ion-concentration of the solutions-as indeed we should expect since the proportion of un-ionized salt is small; but the existing data are too scanty t o admit of any very strict generalization of this character. I n the present work i t was assumed that the absorption-coefficient of CO2 in the carbonate solutions is the same as in sodium chloride of the same equivalent concentration ; this mode of calculation leads to practically the same result as calculation on the basis of equality of absorption in solutions of equal ion-concentration, and is simpler to carry out. The coefficients actually used are given in the appropriate place; they were read from curves drawn on the basis of values interpolated from a large scale plot of Bohr's results in water and solutions of NaC1, as follows: VALUESOF c = ~422.4, WHERE CY IS THE ABSORPTION COEFFICIENT OF Con. Temperature.
In water.
3.5
0.0672
I2
0.0500
In 1 . 1 7 N solution.
In 3.44 N solution.
0.0484 0.0367 0.0328
0.0270 0.0213 0.0193
16
0.0441
25
0.0338
0.0260
0.0159
30 40
0.0297 0.0236
0,0232
0.0142
0.0185
0.0117
The next step is to obtain the value of kl and k2, or more particularly of the ratio k l / k z , which is obtained directly from McCoy's4 work on the carbonate-bicarbonate equilibrium. Walker and Cormack, J . Chem. SOC.,77, 13-14 (1900); see also Walker, Ibid., 839 182 (1903). * C. Bohr, Ann. Physik, 68, 5 0 0 (1899). a G.Geffcken, 2.physik. Chem., 49,257 (1904). 4 H . N.McCoy, Am. Chem. J., 29, 437 (19031.
2004
JOHN JOHNSTON.
The Carbonate-Bicarbonate Equilibrium. On dividing Equation I11 by Equation I V we obtain
r being the ratio of the first to the second ionization constant of HzCO3; whence by combination with V [HCOa-]’ (VII). = nr. [co3”]CP By means of Equation VI1 values of nr can be calculated from McCoy’s data on the equilibrium at 2 5 O between sodium bicarbonate and carbonate in aqueous solutions in contact with a measured partial pressure ( P ) of COZ. Such calculations were made by McCoy; in the present calculation corrections which were indicated by McCoy, but not carried ‘out, have been made for the change of solubility of COZ in salt solutions and for the degree of ionization of the sa1ts.l The latter correction was made on the basis of the principle, now well established,2 that the degree of ionization of a salt in a mixture is sensibly equal to that of a salt of the same valence type a t the same total ion-concentration; this is, a t the least, a more accurate procedure than the direct calculation from the conductivity of solutions of sodium carbonate or bicarbonate, on account of the complexity of the solutions and the consequent difficulty of interpreting the results. McCoy made three series of determinations, all a t 2 5 ’ , the results of which are reproduced in Table I ; in these three series the total concentration of sodium was, respectively, 0.I , 0 . 3 and I .o N. The values of t (the molar absorption of COz) and of y1 and y2 (the degrees of ionization of NaHCOa and NaZC03, respectively) which were adopted follow: Total conc. of Na.
C.
n.
v.
0.81
0.70
1.0
0.0323 0.0295 0.0233
0.76 0.65
0.63 0.56
A.................... 0.1 B. ................... 0.3
c ....................
It will be observed that the values of nr, which are very satisfactorily concordant in each series, decrease with increasing concentration; this decrease, which is too large to be due to simple errors in the values of G and y adopted, may be attributed to failure of the tacit assumptions that n and the activity of the water are ~ o n s t a n t . ~However this may 1 Cf. Stieglitz, Carnegie Innst. Publ., 107,243-5 (1909).
* See, for instance, publications from the laboratory of A. A. Noyes.
It may be noted that if we assume the relative decrease of solubility of COS with increase of salt concentration to be a rough measure of the decrease in activity of the water (as has been done in attempts to estimate the extent of hydration), and calculate on this basis, the three mean values of nr become 5500, 5350 and 5000, respectively. a
2005
CALCIUM A N D MAGNESIUM CARBONATES.
be, we shall adopt here the value of 5600, which is the extrapolated value a t zero concentration when the three above results are plotted; in other words, 5600 = nkl/kz where k , and kz are the first and second ionizationconstants of HzC03.
TABLEI.-vALWS
OF
121
FROM McCoy's DATAON THE = [HC03-12 CALCULATED
[ COa']cP" CARBONATE-BICARBONATE EQUILIBRIUM AT 2 j '.
P.
(Atm.)
0.00161 0.00159 0.00259 0.00294 0.00322 0.00404 0.0223 0.0749
Conc. of total bicarbonate. x.
0.0682 0.0690 0.0760 0.0775 0.0781 0.0818 0.0951 0.0985
IHCOi-]
Conc. of total carbonate.
= Yl I.
Y.
A : x + y = 0.1. 0.0552 0.0318 0.0559 0.0310 0.0615 0.0240 0.0628 0.0225 0.0633 0.0219 0.0662 0.0182 0.0770 0.0049 0.0798 0.0015
[cor==] 1/2YZY.
nr.
0.0111
5260
0.0109 0.0084 0.0079 0 0077 0.0064
5600
=5
a
0.0017 0,0005
5380 5300 5040 5300 48401 5260'
5300
B :x f y 0.00319 0.00583 0.01044 0.0
0.0 0.0
0.0436 0.0624
0.I737
0.2037 0.2307 0,2556 0.2664 0:2778
0. I 0 2 1
0.758 0.810 0,860
0.1682
0.902
= 0.3.
0.132 0.I55 0.176 0.I94 0.203
0.1263 0.0963 0.0693 0.0444 0.0336
0.0398 0.0303 0.0218 0.0140 0.0106
0.211
0.0222
0.0070
C:x+y=1.0. 0.492 0.242 0.190 0.526 0.559 0.140 0.586 0.098
4650 4610 4610 4400 4770 4780
0.0678 0.0533 0,0392 0.0274 3450
Walker and Cormack,2 from concordant determinations of the conductivity of solutions of carbonic acid,' concluded that a t 18'
Omitted in taking the mean because of the small percentage accuracy of [COS'] in those cases. a Walker and Cormack, J . Chm. SOC., 77, 8 (1900). a This value is derived from that a t 18' by means of the van't Hoff formula on the basis that the heat change accompanying the reaction is Z7QQ cal. (Lewis and Randall, THIS JOURNAL, 37, 467 ( I ~ I S ) . )
2006
JOHN JOHNSTON.
where n, as before, is the fractional amount of the total C02 in solution existing in the form of HzC03. Consequently
which is identical with the result originally computed by McCoy (6.o X ~ o - l l ) , with that (6.4X 10-l~) recalculated from the work of Shields' on the hydrolysis of sodium carbonate, and with that obtained by Auerbach and Pick2 (6 X 1 0 - l ~at 18")using still other methods. The above value of nr was determined for a temperature of 2 5 O , but i t may be applied with safety a t other temperatures not too far removed from z jO ; in using this value for other temperatures we are tacitly assuming that nr remains constant-an assumption which, though it may well prove to be far from correct, is the best that can be done so long as the necessary data are unknown. The Solubility-Product Constant. On substituting in Equation VI1 for [COa'] its value from Equation I we obtain finally [&f++] [HC03-I2 = nYKMCP or
Thus the solubility-product constant KM of a carbonate can be calculated if corresponding values of the quantities on the right hand side of Equation VI11 are known; the factors in the numerator can be derived from measurements of the solubility of the carbonate MC03 in presence of COz a t the pressure P by ( I ) correcting for the (always small and frequently negligible) amount of neutral carbonate p r e ~ e n t (, 2~) multiplying the concentration of bicarbonate so obtained by the appropriate value of the degree of ionization, (3) inserting the appropriate values of G and P, and working out. We shall now proceed to some actual cases; but before doing so, we wish to point out that the solubility-product constant (like the solubility itself) has no significance except in relation to a definite solid phase-that this quantity is not the same for the three known forms of CaC03 (calcite, aragonite, vaterite) nor again for MgC03.3H20, Shields, 2. physik. Chem , 12, 167 (1893). Auerbach and Pick, "Die Alkalitat wasseriger Losungen kohlensaurer Sake," Arbeiten kais. Gesundheitsamt., 38, 243 (191I). a As will be evident later, it is not admissible to subtract (as Bodlander did in the case of MgCOa) a constant quantity corresponding to the saturation concentration of the neutral carbonate as measured in pure water; the latter, moreover, is not a definite quantity, for there can be no equilibrium except in presence of a definite pressure of COO 1
2
2007
CALCIUM AND MAGNESIUM CARBONATES.
MgC03.H20 and MgC03 except a t the transition point of one form to the other. The Solubility-Product Constant of Calcium Carbonate (Calcite). In this case there is no doubt as to the nature of the solid phase. Determinations of the solubility of CaC03 a t 16' have been made by Schloesingl a t partial pressures of COz ranging up to I atm. and by Enge12 a t pressures from I to 6 atm. Calculations based on their results are presented in Tables I1 and 111. The first two columns of Table I1 contain the actual measurements of the partial pressure ( P , in atm.) and the total concentration of calcium in the solution (expressed in mols per liter); the quantities in the other columns are derived from these, except that the values of the degree of ionization (y) in the fourth column are those (as derived from the conductivity) of equivalent solutions of calcium acetate. In the third column are given the corrected total concentrations of bicarbonate, from which, by multiplication with the appropriate value of y, the values of [HCOs- ]/2 tabulated in the fifth column were obtained; the sixth column gives the total concentration of calcium ion, which = '/Z[HCO~-] [COi=],and in the last are the computed values of the constant nrKca.
+
TABLEII.-cALCULATIONS
ON THE BASISOF SCHLOESING'S DATAON THE SOLUBILITY CALCITEIN WATERCONTAINING cP MOLS COZ AT 16'; c = 0.0441.
OF
P.
(Atrn.)
Total [Ca]. Total Ca(HC0s)z. Mols I 1. Mols 1 1.
0.000504 0.000746 0.O0O808
0.0008jO
0.00333 0.01387 0.02820 o.oj008
o.001372 0.002231 0.00296j o.003600 0.00j330 0.006634 0.007875 0.008855 0.00972 0.01086
0.1422
0.2538
0.4167 0.5533 0.7297 0.9841
0.000731 0.000837 0.001364 0.00~226 0.00~961 0.003597 0.005328 0.006632 0.007874 0.008854 o.oog72 0.01086
7.
0.906 0.904 0.890 0.870 0.856 0.844 0.822 0.811
0.798 0.790 0.785 0.778
1/2[HCOs-].
[c~++I.
nrWa.
0.000663 0.000678 5.36X IO-^ 0.O0O757 0.000770 4.95 o.001z140.001zzz 4.99 0.001g4o o.oo194j 4.79 0.00zj37 0.002j41 5.28 0.00304j 0.003048 5.10 0.00438 0.00438 5.36 o.ooj38 0.00538 5.57 0.00628 0.00628 5.39 0.00699 0.00699 5.60 0.00763 0.00763 5.52 0.0084j 0.0084j 5.56
5.30 x IO-^
ON THE BASIS OF ENGEL'S DATAON THE SOLUBILITY OF CALCITEIN WATERCONTAINING cP MOLSCOz AT 16'.
TABLE111.-CALCULATIONS P. (Atrn.) I
2
4 6
Total [ Ca]. Mols 1 1.
0.01085 0.01411 0.01834 0.02139
C.
0.0439 0.0438 0.0437 0.0437
y.
0.778 0.756 0.730 0.713
[ ~ a + += ] ~/~[Hco~-I. f i r ~ ~ a .
0.00844 0.01066 0.01338 0.01j25
Schloesing, Comfit. rend., 74, 1552;75, 70 (1872). [6]13, 348 (1888).
* Engel, Ann. cbitim. pkys.,
5.48X IO-& 5.53 5.48 5.41 5 . 4 7 x IO"
JOHN JOHNSTON.
2008
A word is necessary as to the method of correcting for the neutral carbonate present-the correction namely ( = [COa"]) applied in deriving the numbers in the third column from those in the second. From Equation VI1 [HCOs-]2/[COs'] = nrcP = 247P a t 16"; and consequently if a n approximate value of [HC03+]is known in advance, the concentration of COB^] (which relatively is always small) can be estimated. Thus in the most dilute solution (where the correction is greatest) of Table 11, the correction is (0.00134)~/247 X 0.0005 = o.oooo~g.~ It can also be obtained directly as soon as a rough value of the solubility-product constant [Ca++][COa'] is ascertained. The amount of this correction in all the solutions is evident by subtracting the figures in Column 3 (or 5 ) from those in Column 2 (or 6); in the stronger solutions i t is obviously entirely negligible. Table I11 is identical in arrangement with Table 11, except that the relative absorption-coefficients of COz are given in the third column; in this case the correction for neutral carbonate is entirely negligible, so that the total concentrations of bicarbonate are identical with the experimentally determined concentrations in the second column. The constancy of the values tabulated in the last column is surprisingly good, especially in view of the fact that P ranges from 0.0005 atm. (slightly greater than the amount ordinarily present in the air) t o 6 atm. ; in other words, the product remains constant even when the concentration of one of the factors in the equilibrium changes as much as ten thousandfold. The mean value derived from the stronger solutions (where the experimental accuracy is greatest) is 5.50 X IO-^, a value from which we can calculate with confidence the solubility of calcite in water a t 16" saturated with COz a t any pressure up to that a t which calcium bicarbonate would begin to appear as solid phase a t this temperature. Accordingly the solubility-product constant of calcite a t 16 is [Ca+f][C033] = Kc, =
'AXE = 0 .5 98 X
IO-^. It is of little use 5600 to compare this with the "solubility in pure water"2 because, except there be no vapor phase, the latter is meaningless except in relation to a definite partial pressure of COz;3for a definite concentration of COz, in accordance with Equations VI and VII, can exist in equilibrium only with definite This is just about 9% of the quantity which ha5 been considered to represent the solubility of CaCOa in pure water. From this correction the extent of hydrolysis in the peveral solutions can obviously be readily calculated. 1 The most recent determinations of this quantity are by Kendall (Phil. Mag., 23, 957 (I~IZ)),who found a t 2 5 O , 50' and IOO', respectively, 14.3, 15.0 and 17.8 mg. CaCOs per liter. There is of course no assurance that the partial pressure of COS was actually the same a t all temperatures, so that these values are not necessarily even comparable with one another. a
See Table IV.,
fiostea.
CALCIUM AND MAGNESIUM CARBONATES.
2009
concentrations of HC03- and HzC03, and the latter in turn requires a definite partial pressure of COZ.’ Determinations of the amount of CaC03 in solution in presence of COn have also been made by others. Treadwell and Reuter2 made very painstaking analyses of a series of such solutions a t 15 O, but-as is obvious from a perusal of their mode of working-did not secure equilibrium conditions, a fact which is borne out by the lack of constancy of the calculated solubility-product constant. Quite recently Leather and Sen3 made series of determinations a t a number of temperatures between 15’ and 40’; their solutions may have attained equilibrium, but their mode of analysis is unsati~factory.~This was confirmed by the calculations, which yielded very irregular results; the most that one can deduce from them is that the solubility-product constant of calcite probably decreases somewhat with the te.mperature, becoming apparently about 0.5 X 10-8 a t 40’. Seyler and Lloyd5 have also made a series of determinations of the equilibrium between solid calcium carbonate and water and certain dilute salt solutions containing excess of carbon dioxide; they kept the solutions, which were shaken occasionally, for long periods in stoppered bottles completely filled with liquid, and ascertained by titration the concentration of free COZ and of the dissolved carbonate. Unfortunately, however, their experiments were carried out a t “the temperature of the laboratory ;” nevertheless despite this indefiniteness, it seemed worth while to include their results (which have been recalculated so as to conform with the others presented in this paper) because these demonstrate that the solubility-product constant of calcite is not affected by the presence in the solution of small excess amounts of added Ca++ (as CaClz or CaS04) or HC03- (as NaHC03). In this case nrKc, = [Ca++] [HC03’]2/[H2C03], where [HzC03] is the concentration of free COZ in solution as determined by titration; as is evident from the table its value varies about a mean, the general average being 4 . 8 0 X IO-^. Conse4.80 X IO-^ quently Kca = -___ - 0.86 X I O + a t the “temperature of the 5600 Similar remarks with respect t o the equilibrium between sodium carbonate and bicarbonate were made by McCoy (Am. C h m . J.,29, 456ff. (1903)). Treadwell and Reuter, 2. anorg. Chem., 17, 170 (1898). a Leather and Sen, Memoirs Dept. Agric. India, Chem. Series, I, No. 7 (1909). One obvious error is a loss of COZ,because in some cases especially in similar work with MgCOa (see postea), the tptal COz in solution, as given in their tables, is insufiieient to convert all of the base present to bicarbonate. As McCoy notes (Am. Chem. J., 29, 444 (1903)) “Carbon dioxide may readily be lost from solutions rich in bicarbonate, if care be not taken to render them alkaline a t once. Low results were invariably obtained when the bicarbonate solutions were measured into beakers and allowed t o stand, even for four or five minutes, before adding an excess of alkali.” [I Seyler and Lloyd, J. Chem. SOC.,95, 1347 (1909).
JOHN JOHNSTON.
2010
laboratory,” whence one might deduce that this temperature was about 20’. Seyler and Lloyd also investigated the effect of the presence of a small amount of a salt (NaC1, NazS04,MgS04) containing no ion in common with calcium carbonate, and found an increase in the total calcium in solution, in qualitative agreement with theory; by allowing for the undissociated fraction of the several salts present one could indeed calculate the solubility-product constant in these cases too, but such calculations would have little value by reason of the paucity and uncertainty of the experimental data. TABLEIIIa.-cALCULATIONS ON THE BASISOF THE RESULTSOF SEYLER AND LLOYD ON THE SOLUBILITY OF CALCITE I N WATER AND DILUTE SALT SOLUTIONS CONTAINING
Free COz [HsCOa].
0.00269 0.00362 0.0100
o.0114 0.00395 0.00104 0.00181
0.00206 o.00315 0,00455 0.00656 0.00356 o.ooqg4 0.00475 0.00406
[Ca] as Conc. of bicarbon- added salt. ate, Mols 1 1.
7,.
FREECog. [ c ~ + + Ifrom ,I::;?[ Total bicarbonate added salt, [Ca++].
yz. = 1/z[HCO3-].
nrKCa.
Without added salt. 0,00370 . . . . . 0.845 . . . 0.00313 . . . . . 0.00313 4.56 X IO-^ 0.00414 . . . . . 0.840 . . . 0.00348 . . . . . 0.00348 4.66 0.00604 . . . . . 0.816 . . . 0.004gZ . . . . . 0,00492 4.76 0.00657 , . . . . 0.810 . . . 0.00532 . . . . . 0.00532 5.28 I n presence of CaCl2. 0.00306 0.00625 0.788 0.788 0.00242 0.00493 0.00735 4.36 I n presence of CaS04. 0.00244 o . o o r ~ g0.848 0.665 0.00207 o.ooo7g 0.00286 4.71 0 . 0 0 3 0 ~ o.oo119 0.838 0.647 0.00255 0.00077 0.00332 4.77 0.00316 o.oo11g 0.837 0.644 0.00265 0.00077 0.00342 4.66 0.00362 o.0011g 0.831 0.633 o.00301 0.00076 0.00377 4.34 0.00441 0.OOIIg 0.821 0.615 0.00362.0.00073 0,00435 5.01 0.004gz o.oo11g 0.815 0.605 0.00401 0.00072 0.00473 4.64 0.00350 0.00312 0,832 0.636 0.00291 0.001g8 0.0048g 4.65 0.00379 0.00625 0,829 0.629 0.00314 0.00394 0.00708 5.66 I n presence of NaHC03. 0.00278 0.00625 0.817 0.817 0 . 0 0 2 2 7 0 . 0 0 5 1 1 0.00965~ ~ 4.45 o.00170 0.0125 0.798 0.798 0.00136 0.010oo~0 . 0 1 2 7 2 ~ 5.42 General mean, 4.80 X I O +
A knowledge of these constants renders unnecessary experimental work such as that of Keiser and M~lL’Iaster,~ who investigated the ratio of the excess of COz in solution to the amount of CaC03. And the fact of this constancy is sufficient reply to statements such as the following: “While there is some evidence which supports the view that calcium bicarbonate exists in the dissolved state, the observed facts can be regarded just as logically and more conveniently as the result of the specific solvent power of the carbon dioxide-water mixture.”4 [HC03-] from added salt. Total [HCOa-]. a Keiser and McMaster, THISJOURNAL, 30, 1714 (1908). 6 Cameron and Robinson, J . Physic. Chem., 1 2 , 573 (1908). 1
CALCIUM AND MAGNESIUM CARBONATES.
201 I
The Solubility of Calcite in Water in Contact with the Atmosphere. The amount of calcium carbonate which will dissolve in water in contact with the air, and the variation of this solubility with the COZ content of the air, are of very great importance in connection with a number of geological processes of very widespread occurrence. The saturated solution of calcite under these conditions is so dilute that the concentration of C03" (and even of OH-) is not negligible in summing up the total concentration of negative ions ; consequently the calculations can be carried out only by a series of approximations. One has namely t o determine values of [Ca"], [HC03-], [COS'] and [OH-], which shall simultaneously satisfy the condition [Ca"] = 1/2[HC03-] [COS'] i'/z[OH-] and three of the following equations:' (I). [Ca++][CO3'] = Kc, = 0.98 X I O - * (VII). [HC03-]2/[C03=]= nrcP = 247 P (VIII). [Ca++][HCO3-I2=nrKcacP = 2.425 X IO-^ P (IX). [OH-]/[HC03-] = K,/nklcP = 3.730 X 1o-'/P (X). [OH-]2/[C03'] = K2,/nklk2cP = 3.435 X IO-"/P I n order to obtain the total concentration of calcium in the solution from the ion-concentrations obtained in this way one must correct for the ionization of the Ca(HC03)z;Z this can be done by dividing the value of l / 2 [HC03-] by the appropriate fractional ionization (TI), the latter being read by inspection from a curve obtained by plotting the fractional ionization-as derived from the conductivity of solutions of calcium acetateagainst the concentration of Ca++. The results derived in this way for various partial pressures of C 0 2 such as may occur in atmospheric air are presented in Table IV. The amount of COZ in ordinary air, which is about 3 parts in 10,000, corresponds, on the basis of Table IV, to about 63 parts CaC03 per million; and, as is evident from the table, comparatively small changes in the concentration of COZ in the air may, in nature, easily bring about the solution or deposition of very large quantities of calcium carbonate. Its solubility would of course be slightly different in natural waters-springs, rivers or the sea; the presence of other calcium salts would make it smaller
+
The numerical values refer to calcite a t 16",where c = 0.0441. Equation IX is obtained by combination of (111) and (V) with the relation [H+] [OH-] = K w = 0.5 X 1 0 - l ~a t 18'; (X) by combination of (VII) and (IX). It may be noted that, for the purpose of these approximations, the various equations must be absolutely consistent; hence it is necessary to retain a larger number of figures than is warranted by the accuracy of the several constants, until the final result is written down. The concentrations of COB' and of OH- are so small that ionization is practically
complete,
2012
J O H N JOHNSTON.
by an amount readily calculable, while salts of other radicals would of themselves make it somewhat larger. It would lead too far to discuss satisfactorily this question here, and its bearing on a number of geologic phenomena.’ It may be affirmed, however, on the basis of analyses cited by F. W. Clarke,2 that many natural waters are substantially saturated with calcium carbonate; while it is certain that the surface layers of the larger part of the ocean, except possibly in the Arctic and Antarctic, must in general be substantially saturated. TABLEIV.-THE CALCULATED SOLUBILITY OF CALCITE IN WATERAT 16’ IN CONTACT WITH AIR CONTAINING THE PARTIAL PRESSURE P OF COz. p.
[Ca’’].
I/,[HCOa-].
71.
[Ca] as Ca(HC0a)n.
ICOr’j.
[OH-I.
0.000488 0.919 0.000532 O.oooOI9 1.82x 0.000527 0.917 0.000574 o.oooo18 1.57 0.000561 0.915 0.000613 o.ooo017 1.40 0.00035 o.oo0608 0.0oogg1 o.gr4 0.000647 o.oooo16 1.26 0.00040 o.ooo635 0.000618 0.913 0.000677 o.oooo16 1.15 0.00045 0.000659 o.ooo643 0.912 0.000705 O . O O O O I ~1.07 0.00050 0.000682 0.000666 0.912 0.000731o.oooo14 1.00 0.00020 0.00050Q 0.00025 0.000546 0.00030 0.000579
Total [Ca].
Parts CaCOa per million.
0.000721
55 59 63 66 69 72
0.000746
75
0.000552
0.000593 0.000631 0.000664 0.000694
The concentration of OH-, tabulated in the seventh column of Table IV, which is a measure of the alkalinity of the solutions, increases with diminishing partial pressure of COZ; indeed purposive variation of the proportion of COZover a solution in contact with excess of calcium carbonate might, in some instances, prove a convenient method of establishing and controlling a definite alkalinity in the solution. Such an action apparently goes on on a large scale continuously in the sea, the alkalinity3 of which corresponds closely to that of the saturated solution of CaCOa in equilibrium with air containing three parts C02 per 10,000. The Solubility-Product Constant of MgC03.3H20(Nesquehonite). Determinations were made by Enge14 of the equilibrium between MgCOs.3Hz0, water, and (a) COZa t pressures ranging up to 6 atm. a t IZO and (b) C02 a t I atm. a t temperatures ranging up 5 0 ~ these ; ~ 1
This will be treated
* F. W.
in another paper now in preparation. Clarke, “Data of Geochemistry,” U. S. Geological Survey, B d l . 491
59ff.(1911). ‘See Ruppin, “Die Alkalinitat des Meerwassers,” 2. anorg. Chem., 66, 122-56 (IQIO), who gives numerous references. 4 Engel, Ann. chim. phys., [6]13, 353, 354 (1888). He also gives a series of preliminary results for pressures ranging up to 9 atrn. a t 19.5O, with “magnesium hydrocarbonate” a~ solid phase, which when calculated give quite a fair constant; these have not been included because the nature of the solid phase a t equilibrium is doubtful. Similar determinations have been published very recently by Leather and Sen (Memoirs Dept. Agric. Iadia, Chem. Series, 3, No. 8 (1914);but-apart altogether from the circumstance that it is very questionable whether equilibrium was really attained in their experiments-their analytical results cannot be trusted, since the
2013
CALCIUM AND MAGNESIUM CARBONATES.
form the basis for the figures presented in Tables V and VI. These tables are identical in arrangement with Table 111, as the correction for [COa-] is absolutely negligible a t the concentrations in question ; the absorptioncoefficient is that for solutions of sodium chloride of equivalent concentration a t the particular temperature, the fractional ionization is that of an equivalent solution of magnesium chloride. TABLEV.-cALCULATIONS ON THE BASIS OF ENGEL'SDATAON THE SOtUBILITY OF MgCOa.3HpO IN WATER CONTAINING CP MOLScoz AT 12 '. P (Atm.)
Total [Mgl. Mols I 1.
0.5
0.255
I
0.326 0.379 0.417 0,443 0 * 474 0.519 0.612
1.5 2 2.5
3 4 6
Ionization. C.
7.
0.0431 0.0418 0.0406 0.0399 0.0393 0.0388 0.0379 0.0362
0.686 0.680 0.675 0.672 0.670 0.669 0,666 0.662
[Mg++]
-
[HCO#-]/Z.
nrKMg.
.06 .os
0.175
I
0.222
I
0.256
I.IO
0.280
I . IO
0.297 0.317 0.346 0.404
I
.07 .og I .og I.l9 I
I
.08
ON THE BASISOF ENGEL'S DATAON THE SOLUBILITY OF MgCOs.3HzO IN WATER CONTAINING C MOLS AT SEVERAL TEMPERATURES. Total [Mg]. y. [Mg"] [HCOa-]/Z. nrKMg at
TABLEVI.-cALCULATIONS
coz
L.
Mols 11.
C.
3.5
0.422 0.326 0.262 0.237 0.187 0.140 0.113
0.0525
I2
I8 22
30 40 50
0.0418 0.0363 0.0328 0.0273 0.0223 0.0186
0.672 0.680 0.686 0.690 0.700 0.715 0.725
-
'.
0.283
1.73
0.222
I
0 . I80
0.164 0.131
0.64 0.54 0.33
0.100
0.18
0.082
0.I 2
-05
From the last column of Table V it is evident that we have a .very satisfactory constant, a constancy which is the more' remarkable in view of the fact that the total ion-concentration of the solution is so largeabove 0 . 5 M throughout. This constancy inclines one to the belief that the solubility-product constant will,when the experimental results can be properly interpreted, be found to hold for substances, the saturated solutions of which are not extremely dilute.2 From the mean value the ratio of the total amount of COZ in the solution (as given by them) t o the magnesia is very irregular and in many cases is even less than 2. (Cf. footnote 4, p. 2009.) Moreover, their results when plotted directly show great inconsistencies. I n accordance with this the calculated values of the product n f K M g are very irregular and show no approach to constancy. 1 On the basis of its value at 18' in each case; but this introduces no appreciable error, since the variation in extent of ionization is very small a t temperatures up t o 50'. (See, for instance, Noyes and Johnston, TEISJOURNAL, 31, 987 ( ~ g o g ) . ) * It may be added that the fact of this constancy is a criterion of the substantial accuracy of the y values chosen; for a change of 3% in the values assigned to y suffices
2014
JOHN JOHNSTON.
product
KMg =
[Mg++][COa']
=
1.08 -
- 1.93 X IO-^ a t
~
12'
when
5600
the solid phase is MgC03.3H20.' From the numbers in the last column of Table VI, the values of the solubility-product constant were calculated ; these are reproduced in Table VII, alongside values calculated from an equation which was derived as follows: If we integrate the well-known equation lnK/dT = Q/RT2 on the basis that Q (the heat effect of the reaction considered) is constant over the temperature range, we obtain 1nK = (-Q/RT) C, which has the form log K = (A/T) B; or, in other words, when values of log K are plotted against I/T, the graph is a straight line. The plot of the data proved to be a straight line, the equation to which is log K = (2315/T) - 11.870. (XI). The agreement between the values calculated directly and those derived from Equation X I is very good, all things considered. Moreover, by comparing the above equations, we can calculate Q-namely (2 = -23 15 X 2.303 R = -10600 cal.; that is, the heat change corresponding to the reaction MgC03.3H20 = Mg" COa= 3Hz0 is an evolution of 10600 cal.
+
+
+
TABLEVII.-THE
+
SOLUBILITY-PRODUCT CONSTANTOF MgC03.3H20 AT VARIOUS
-
TEMPERATURES. KMg
12
T. 276.5 285
18
291
22
295 303 b I3 323
t.
3.5
30
40 50
Derived from Table VI.
3.09 X I .88 I.14 0.97
10-4
[Mg++][COs']. Calc. from Equation XI
3.17 X 1.78 1.21
0.32
0.95 0.59 0.33
0.21
0.20
0.59
IO-(
T h e Solubility of MgC03.jH20 in Water in Contact with the Atmosphere, and the Question of Basic Magnesium Carbonates.-The figures in Table VI1 enable one to calculate, in precisely the same way as was to produce a pronounced trend in the values of wKM,. Conversely, careful work of this character could be used as a means of determining the extent of ionization, which would be practically independent of the assumptions made in the usual methods of deriving this quantity. To avoid misconception, it may be remarked that the values of y as given in the table were all chosen before any of the calculations of the value of nYKMg were made. 1 The solubility of MgC03.3H20in "pure water" is given by Auerbach (2. Elektrochem., IO, 161 (1904)) as 0,0095 mol per liter a t IS', 0.0087 a t q 0 ,and 0.0071a t 35 "; but these results are again indefinite for the reason already pointed out (p. 2008). In this case, as it happens, the process of hydrolysis goes on quite slowly a t ordinary temperatures.
CALCIUM AND MAGNESIUM CARBONATES.
2 0 1j
done for calcite, the total solubility of MgC03.3H20a t temperatures up to 50' in water in contact with any partial pressure of COZ; but in this case the sparing solubility of Mg(OH)2 introduces an added complication which enters whenever the partial pressure is reduced t o a definite limiting value, the magnitude of which depends upon the temperature. In order to'bring out this point, which has a very important bearing on the composition of basic carbonates of magnesia, we shall make the calculations for 18" and partial pressures ranging from o.oooz to 0.0005 atm. One has again to determine values of [Mg++], [HCOa-I, [COa'] and [OH-] which shall satisfy the condition [Mg"] = '/z[HC03-] -I[COa'] 1/2[OH-], two of the following equations:' (VII). [HC03-]2/[C03'] = nrcP = 229.6 P (VIII). [Mg+f][HC03-]2 = lZ?'KMgCP = 2.755 x IO-' P (IX). [OH-]/[HCOs-] = K,/nklcP = 4.012 X IO-' P (X). [OH-I2/[COa=] = K2,/nklkzcP = 3.694 X ~ o - l ' / P and either (I). [Mg++][C03'] = KMg = 1.2 X IO-^ or (XII). [Mg+'][OH-]2 = 1.2 X 10-l' The choice between (I) and (XII) is not an arbitrary one, but depends uppn the value of P. For by combination of Equations I and X (or VI11 and IX), one obtains the relation
+
a value which exceeds the product XI1 whenever P is less than 0.000369. Consequently, when P is less than 0.000369, the solid phase in equilibrium with the solution a t 18' is not MgC03.3H20,but Mg(0H)'; in other words, this is a type of transition pressure, both solid phases being in equilibrium with the solution when the COzpressure is exactly 0.000369 atm. This transition pressure increases rapidly with rise of temperature because K2,/nklkz increases rapidly while K M g / cvaries little ; the increase cannot, however, be calculated because the rate of increase of kz with temperature is not known. From the values of the ion-concentrations computed by means of the above equations, the total amount of magnesium in solution was obtained by correcting for the ionization of Mg(HCO& and MgC03 a t their respective concentrations. This was done by dividing the value of ( a ) l/~[HC03-] (b) [C03'] by the appropriate fractional ionization (7'and y z , respectively), which was read from a curve obtained by plotting the fractional ionization-as derived from the conductivity of solutions of (a)
* The numerical Cf. p.
values refer to MgC03.3H90 at 18'; c has been taken as 0.041.
2011.
* This value is the lower of the two given in Landolt-Bornstein-Roth Tabellen; it is due to Dupr6 and Bialas (2.angew. Chem., 16,jj (1903)).
2016
JOHN JOHNSTON.
MgCl2 (b) MgS04-against the concentrations of Mg". of these calculations are presented in Table VIII.
The results
TABLEVIII.-THE CALCULATED SOLUBILITY OF MgCOs.3H10 IN WATER AT 18' CONTACT WITH AIR CONTAINING THE PARTIAL PRESSURE P OF CO,. P.
[Mg++l. [HCO8-]/2.
[Cos'].
[OH-]
XlO-6.
0.01275 0.00765 o,mogog 3.07 0.01454 0.00895 0.000558 2.87 0.00030 0.01620 0.01017 0.000602 2.72 0.00035 0.01775 0.01134 0.000640 2.60 0.00040 0.01862 0.012170.0006eq 2.44 0.00045 0.01906 0.01275 0.000630 2.28 0.00050 o.org47 0.01330 0.000616 2.13
0.00020
0.00025
[Mgl as 71. Mg(HC0s)a.
72.
0.827 o.oog25 0.505 0.820 0.01091 0.495 0.815 0.01247 0.486 0.810 0.01400 0.477 0.807 0.01506 0.473 0.805 0.01583 0.470 0.804 0.01655 0.467
&&
IN
Total
[Mg].
0.01008 0.01g34 0.01126 0.02218 0.01238 0.02486 0.01341 0.02742 0.01361 0.02868 0.01340 0.02924 0.01320 0.02976
The last column gives the total concentration of magnesium in solution a t 18' a t the several partial pressures, the solid phase in equilibrium with the solution being MgCO3.3H20 a t pressures above 0.00037, but Mg(OH)2 when the pressure of COz is less than 0.00037. Accordingly, if we keep the C02 pressure constant a t P and evaporate off the water a t I 8 O so slowly that equilibrium conditions are continuously attained, we shall obtain the following amounts of either Mg(0H)B or MgCOa.3HzO from one liter of the solution: TABLEIX. Mg(0H)I.
P.
Total [Mgl.
g.
0.00000 0.00020 0.o0025
0.ooorg
0.0087
0.01934 0.02218 0.02486 0.02742 0.02868 0.02924 0.02976
1.13 I .29 1 a45 I .60
0.00030 0 * 00035 0.00040 0.00045 0.00050
.... .... ....
MgC01.3&0.
B.
....
.... ....
.... 3.97 4.05
4.12
If the constant pressure were exactly the transition pressure, both solid phases would be formed; but if it is slightly above or below this limit, either carbonate or hydroxide would separate when the water is evaporated off. At higher temperatures this transition pressure is, as noted above, higher. From the foregoing i t is obvious that the ordinary methods of preparing magnesium carbonate (in which, it is safe to say, a state of equilibrium is not attained continuously) will yield a product contaminated with hydroxide, the amount of which will depend upon the mode of working generally, and upon the prevailing partial pressure of COz over the liquid in particular ; moreover, that this contamination can be avoided completely by working with a partial pressure P greater than a certain limit. This limit is readily calculable in each particular case from the equations on p. 2015;and without doubt one could easily devise a process of preparing
CALCIUM AND MAGNZSIUM CARBONATES.
2017
pure MgC03 in which one atmosphere of COZ would suffice to prevent the precipitation of hydroxide. The quantitative results presented above may require modification by reason of the possible inaccuracy of some of the data involved; of these the one most open to question is the solubility of magnesium hydroxide in pure water, which would tend to be found too high owing to the circumstance that the amount of magnesium present in solution in contact with magnesium hydroxide is increased more than a hundredfold when the atmosphere in contact with the solution contains as little as 2 parts COZ per 10,000(see Table IX). Again the results given are subject to the limitation that the only solid phases are MgC03.3HzO and Mg(0H)z; when conditions are such that one solid phase is MgC03.HzO or MgG03, the appropriate solubility-products (which a t present are not known, and differ from one another, except a t the mutual transition points) must be employed. Moreover, if within any temperature or pressure range a definite crystalline basic carbonate should be capable of stable existence in contact with water,' it would have to be taken into account in calculations relative to those conditions. I n any case the general conclusions derived from these theoretical considerations are in complete accord with the established behavior of magnesium carbonate,2 and in particular give a rational way of accounting for the well-known indefinite character of the ordinary basic carbonates of magnesia. The Deposit from Solutions Containing both Calcium and Magnesium Carbonates. In any solution saturated with respect to both calcite and MgC03.3H20 the ratio of the concentrations of Mg++ and Ca++ must have a definite value; for instance, a t 16') this ratio is
So long as MgC08.3H20 is the second solid phase this value is independent of the partial pressure of COz, and varies relatively little with the temperature. From the foregoing it follows that if a solution containing only calcium and magnesium carbonates is evaporated down (or if the partial pressure of COZ is gradually reduced, or if both things happen simultaneously) a t 16O, pure calcium carbonate3 will precipitate so long This is equivalent to the condition that such a basic carbonate should have a definite solubility in water or water containing Con, it being the only solid phase present; this implies that its molar solubility must be less than l / z s 4 F h , where Kh is the solubility-product constant of Mg(OH)*a t the temperature in question, for otherwise Mg(0H)Z would be precipitated and two solid phases would be present. See, for instance, Abegg's Handbuch, 11, 2, 66-9 (1907). Under certain circumstances this might come down as aragonite instead of calcite; but this makes no difference in principle to anything here stated, for the solubility of aragonite is apparently only about 10% greater than that of calcite. This whole question is being taken up in another paper now in preparation.
2018
JOHN JOHNSTON.
as the above ratio is less than 14000, as it would normally be in natural waters, provided always that the COZ pressure is sufficient to prevent precipitation of magnesium hydroxide; on the other hand, the order of precipitation will be reversed if the relative concentration of magnesium ion be greater than 14000 ( e . g., by addition of a soluble magnesium salt). It is to be emphasized however that the foregoing deductions, which are valid only if the only solid phases separating are pure calcite and pure MgC03.3Hc0, would have to be modified if, for instance, MgC03 can occur t o a slight extent in solid solution with calcite, a possibility suggested by certain geological observations. But we have another state of affairs if the partial pressure of COZ is such that magnesium hydroxide may precipitate ; and in actual practice this case may very readily occur, since the hydroxide appears when the partial pressure of COZ is about o.00037, a proportion which is somewhat greater than that normally present in outside air. This again can be readily calculated. By combination of Equations I and X we obtain the relation
a t 16'; consequently for values of P less than 0.00037, [Mg"] -
[Ca++]
- [Mg"][Oz
[Ca++][OH-I2
-
X IO-"P 3.5 3.43 X I O - ~ ~
1.2
x
IO'P,
a ratio which decreases steadily as P is reduced. It follows from this that calcium carbonate precipitated from a solution containing magnesium may very readily be contaminated with appreciable proportions of magnesium hydroxide, which would be removed only slowly by repeated reprecipitations. That this actually occurs in the commercial manufacture of calcium carbonate is evident from the experience of Hostetter,' who found it a matter of considerable difficulty to buy calcium carbonate satisfactorily free from magnesia. But this trouble may be obviated very easily, namely by conducting the operations in such a way that the liquid is always saturated with COz a t a pressure above a certain limiting value ; this limit, which increases with the temperature, cannot a t present be specified very accurately, but is in all probability not greater than I atm. for any conditions likely to be encountered in actual practice. Further discussion of the deposits resulting from the concentration of solutions containing both calcium and magnesium carbonates will be deferred for the present, as it necessitates the consideration of the solubility, and proneness to supersaturation, of the several forms of calcium and magnesium carbonates, as well as of the double carbonate dolomite;
* J. C. Hostetter, J. Ind. Eng. Cltem., 6,392 (1914).
CALCIUM AND MAGNESIUM CARBONATES.
2019
and the evidence on some of these points is unsatisfactory or lacking altogether. The Solubility-Produc t Constant of other Carbonates. For the sake of completeness, the solubility-product constant of barium carbonate has also been recalculated. The data, which again are due to Schloesing, and the derived quantities are presented in Table X, which is altogether similar to Table 11,except that the ionization is, in this case, that of barium acetate a t the equivalent concentration. The mean value from the six last experiments is nrKBa = 3.95 X IO-^, whence [Ba++][COs']
=
7 . 0 X IO-^ a t 16'.
TABLE X.-CALCULATIONS ON OF
BaC03
IN
THE BASISOF SCHLOESING'S DATAON THE SOLUBILITY WATER CONTAINING CP MOLScoz AT 16'; C = 0.0441.
(Atm.)
P.
Total [Ba]. Mols I 1.
Total [Ba(HCOs)zl. Mols 1 1.
0.000504 0.000808 0.00333 0.01387
0.000601 O.ooO732 0.00117 0.00196
0.000589 0.000722 0.00116 0.00196
0.0282
0.00255
0.00255
0.0499 0.1417 0.2529 0.4217 0.5529 0.7292 0.982
0.00312 0.00464 0.00578 0.00690 0.00766 0,00843
0.00312 0,00464 0.00578 0.00690 0.00766 0.00843 0.00941
0,00941
Y.
0.930 0.924 0.915 0.895 0.884 0.875 0.850 0.838 0,825
0.818 0.811 0.802
IBa++I.
ZYKBa.
0,000548 0.000667 0.00 1065 0.00175
0.000560 0.000677 0.00107 0.00175
0.00225
0,00225
0.00273 0.00394 0.00485 0.00570 0.0062 7 0.00684 0.00755
0.00273 0.00394 0.00485 0.00570 0.00627 0.00684 0.00755
3.02 X IO-^ 3.38 3.31 3.51 3.66 3.70 3.92 4.09 3.98 4.05 3.98 3.98
[HC03-]/2.
3.95
x
Io-6
The constants of two other carbonates are known approximately;' namely, for silver carbonate,2 for which it is about 10-l~~ and for lead ~ a r b o n a t e ,about ~ I 0 -14.
Summary. The solubility-product constants of calcium carbonate (calcite) and of magnesium carbonate (MgC03.3H20), a knowledge of which is of importance in connection with several problems of geological interest, have been recomputed from the best experimental data available ; the results are satisfactorily concordant. This concordance is the more remarkable in view of the fact that in the case of the data for calcium carbonate the Approximately only, because the partial pressure of COZ(which, however, would be small) was neither controlled nor measured. a Abegg and Cox, Z . physik. Chem., 46, 1 1 (1903);Spencer and Le Pla, Z. anorg. Chem., 65, 14 (1910).It would be well worth while to repeat these measurements under carefully controlled conditions, especially a t a series of temperatures; for a number of important deductions could be drawn from the results. 3 Pleissner, Arbeiten kais. Gesundheitsamt, 26, 30 (1907).
JOHN JOHNSTON.
2020
partial pressure varies more than ten-thousandfold; while the total ionconcentration of all the magnesium carbonate solutions on which the actual solubility determinations were made, was more than 0 . 5 N. The recalculated results are: [Ca++][C03=]= 0.98 X IO-* a t 16', when the solution is saturated with respect to calcite; [Mg"] [COS'] = I . 93 X IO-^ a t 12 O , the solution being saturated with MgC03.3H20;[Ba++][COa"] = 7 X IO-^ a t 16', the solid phase being BaC03. The solubility-product constant K M of~ MgC03.3H20 a t temperatures up t o 50' is given by the formula log K M = ~ 2315/T - I I . 870,
-
whence the heat change corresponding to the reaction MgC03.3H20
Mg++
+ COS" + 3Hz0
is an evolution of 10600 cal. With a knowledge of these constants and of the solubility-product constant of magnesium hydroxide, one can show that calcium carbonate precipitated from solutions containing magnesium is likely to be contaminated with small quantities of magnesium hydroxide which could be removed only slowly by reprecipitations as ordinarily carried out ; that mixtures of magnesium carbonate and hydroxide will in general be obtained in the precipitation of magnesium by a carbonate and that the basic carbonates thus produced are merely indefinite mixtures of carbonate and hydroxide; and that both calcium and magnesium carbonates can be obtained free from contamination by keeping the partial pressure of carbon dioxide above a certain limiting value, the magnitude of which depends upon the conditions and in all probability need not be greater than I atm. by a suitable choice of mode of operation. Incidentally the constant [HC03-]2/[C08c][H~C03] was recalculated from McCoy's data, and found to be 5600 n a t 25', where n (which is in all likelihood greater than 0.5) is the proportion of the total COn in solution which exists as HzC03; whence kz, the second ionization constant of carbonic acid, is 6 X ~ o - l l ,identical with the accepted value of this constant. It may be pointed out, moreover, that there can be no real equilibrium in aqueous solutions of carbonates except in presence of a definite partial pressure of C 0 2 in the atmosphere in contact with the solutionin other words, that, strictly speaking, we are dealing with a ternary system, namely, base-C02-Hz0 ; consequently any carbonate solution through which a stream of gas absolutely free from COz is passed, would gradually lose its carbonate and ultimately would contain only hydroxide. GBOPHYSICAL LABORATORY. C A R N E G l s INSTITUTION OF WASHINGTON.
WASHINGTON. D. C.
